Année

ISBN

URI

Collections

Métadonnées

Auteur

Lehtonen, Erkko

Couceiro, Miguel

Couceiro, Miguel

Type

Communication / Conférence

Nombre de pages du document

65-72

Résumé en anglais

Let A be a nite set and B an arbitrary set with at least two
elements. The arity gap of a function f : An ! B is the minimum decrease in
the number of essential variables when essential variables of f are identi ed.
A non-trivial fact is that the arity gap of such B-valued functions on A is at
most jAj. Even less trivial to verify is the fact that the arity gap of B-valued
functions on A with more than jAj essential variables is at most 2. These
facts ask for a classi cation of B-valued functions on A in terms of their arity
gap. In this paper, we survey what is known about this problem. We present
a general characterization of the arity gap of B-valued functions on A and
provide explicit classi cations of the arity gap of Boolean and pseudo-Boolean
functions. Moreover, we reveal unsettled questions related to this topic, and
discuss links and possible applications of some results to other subjects of
research.